Timeline for Computing Grothendieck group of coherent sheaves of affine toric 3-fold from a simplicial cone
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| Aug 30, 2023 at 17:10 | comment | added | Boris | @ David E Speyer Thank you very much for your kind help. | |
| Aug 30, 2023 at 17:03 | comment | added | David E Speyer | But the more general question of understanding what $G_0(X)$ DOES look like in this case seems worthwhile, so I'm not leaving an answer on the assumption that someone else will answer that question. | |
| Aug 30, 2023 at 17:02 | comment | added | David E Speyer | To the specific question about $e_1$, $e_2$, $(0,b,c)$, no. Consider the cone with rays $(1,1,-1)$, $(1,-1,1)$, $(-1,1,1)$. For any two of these rays $\rho$ and $\sigma$, the point $(1/2) (\rho+\sigma)$ is in $\mathbb{Z}^3$ but not an integer combination of $\rho$ and $\sigma$. So no $GL_3(\mathbb{Z})$ matrix can transform $\rho$ and $\sigma$ to $e_1$ and $e_2$. | |
| Aug 30, 2023 at 15:52 | history | asked | Boris | CC BY-SA 4.0 |